src/ZF/Nat.thy
author clasohm
Tue Feb 06 12:27:17 1996 +0100 (1996-02-06)
changeset 1478 2b8c2a7547ab
parent 1401 0c439768f45c
child 2469 b50b8c0eec01
permissions -rw-r--r--
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     1 (*  Title:      ZF/Nat.thy
     2     ID:         $Id$
     3     Author:     Lawrence C Paulson, Cambridge University Computer Laboratory
     4     Copyright   1994  University of Cambridge
     5 
     6 Natural numbers in Zermelo-Fraenkel Set Theory 
     7 *)
     8 
     9 Nat = Ordinal + Bool + "mono" +
    10 consts
    11     nat         ::      i
    12     nat_case    ::      [i, i=>i, i]=>i
    13     nat_rec     ::      [i, i, [i,i]=>i]=>i
    14 
    15 defs
    16 
    17     nat_def     "nat == lfp(Inf, %X. {0} Un {succ(i). i:X})"
    18 
    19     nat_case_def
    20         "nat_case(a,b,k) == THE y. k=0 & y=a | (EX x. k=succ(x) & y=b(x))"
    21 
    22     nat_rec_def
    23         "nat_rec(k,a,b) ==   
    24           wfrec(Memrel(nat), k, %n f. nat_case(a, %m. b(m, f`m), n))"
    25 
    26 end